Question

in the figure below, m ∠ 2 = 129°. find m ∠ 1, m ∠ 3, and m ∠ 4.

m ∠ 1 = □°
m ∠ 3 = □°
m ∠ 4 = □°

Explanation:

Step1: Find \( m\angle1 \)

\( \angle1 \) and \( \angle2 \) are supplementary (they form a linear pair), so their measures add up to \( 180^\circ \).
\[
m\angle1 + m\angle2 = 180^\circ
\]
Substitute \( m\angle2 = 129^\circ \):
\[
m\angle1 + 129^\circ = 180^\circ
\]
\[
m\angle1 = 180^\circ - 129^\circ = 51^\circ
\]

Step2: Find \( m\angle3 \)

\( \angle3 \) and \( \angle1 \) are vertical angles, so they are equal.
\[
m\angle3 = m\angle1 = 51^\circ
\]

Step3: Find \( m\angle4 \)

\( \angle4 \) and \( \angle2 \) are vertical angles, so they are equal.
\[
m\angle4 = m\angle2 = 129^\circ
\]

Answer:

\( m\angle1 = \boldsymbol{51}^\circ \)
\( m\angle3 = \boldsymbol{51}^\circ \)
\( m\angle4 = \boldsymbol{129}^\circ \)